Simplify the following expression: $r = \dfrac{-20y^2 + 40y}{-65y}$ You can assume $y \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-20y^2 + 40y = - (2\cdot2\cdot5 \cdot y \cdot y) + (2\cdot2\cdot2\cdot5 \cdot y)$ The denominator can be factored: $-65y = - (5\cdot13 \cdot y)$ The greatest common factor of all the terms is $5y$ Factoring out $5y$ gives us: $r = \dfrac{(5y)(-4y + 8)}{(5y)(-13)}$ Dividing both the numerator and denominator by $5y$ gives: $r = \dfrac{-4y + 8}{-13}$